math final 2007 fall

B find the number of units produced which will result

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Unformatted text preview: al cost. What is the minimum total cost? 15. (6 points) Find the antiderivatives. (a) x 2 3x 1 dx (b) x3 x 2 6 x 10 3 dx Solutions x1x1 1. (a) lim x lim x9x1 1 x 1 5x2 6 x 3 (b) lim x x 1 2 x3 3x x3 x2 x (c) lim x4 x4 x 2. (a) f (b) lim x f 0 f 4. x1 f 3x 6 2 lim f h (b) Rewrite as x xh lim 10 x 2 x 2 6 4 6 (the 2-sided limit exists) 4 5x h 4. x2 5x 3 3 h 0 lim h h 2x h 5 0 2x 0 5 6 mT f 2 7x 2 1/ 3 7 x4 ln x5 1 fx 2 4 lim f x 2x h 5 0 y6 d e5 x dx x 1 4 lim f x x lim 2 mT x x1 4 4) 6 h h y1 f x and 6 1 The function f is discontinuous at x fx 2 xh h h x 2x 5 dy dx x 0 lim x 9 x 2 18 x 7 x x4 4 h 5h 0 2 y y1 5. (a) 4 4 fxh 2 h 000 200 x4 lim f x 4 lim lim 7 x3 10 x3 4 x (c) lim f x h x 6 x2 3 x2 2 lim 2 4 x x 2 lim f x 3. f lim 10 4 x 5 x 7 lim f x x 1 5 6 (the function is def...
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